Phase contrast x-ray interferometry

ABSTRACT

A phase contrast X-ray imaging system includes: an illumination source adapted to illuminate a region of interest; a diffraction grating adapted to receive illumination from the illuminated region of interest, the diffraction grating comprising a spatial structure having a first periodicity superimposed with a second periodicity that is different from the first periodicity; and a detector adapted to detect illumination passing through the diffraction grating, wherein the spatial structure is defined by varying height and/or pitch, and wherein the spatial structure imparts a first phase dependence based on the first periodicity and an additional phase dependence based on the second periodicity on the illumination passing through the diffraction grating.

CROSS-REFERENCE TO RELATED APPLICATION

This application claims priority to U.S. Provisional Application No.62/536,321 filed Jul. 24, 2017, the entire content of which is herebyincorporated by reference.

BACKGROUND 1. Technical Field

The field of the currently claimed embodiments of this invention relatesto X-ray imaging, and more particularly to phase contrast X-rayinterferometry.

2. Discussion of Related Art

Conventional X-ray images the attenuation coefficient of materials andbiological tissue. Phase-contrast X-ray adds two other aspects, usingcoherent X-ray: imaging the phase-shift and the scattering of X-rayimaging (dark-field). Whereas conventional X-ray imaging measures theattenuation coefficient of an object, phase contrast (PC) X-rayinterferometry systems measure the real part of the refractive index ofan object. This can thus be used for material science andnon-destructive testing and medical imaging [1-25]. For medical imagingthe real part of the refractive index lends significantly (˜1000 times)higher soft-tissue (low-Z) contrast [3]. Two major directions ofinvestigation that have made great strides are Talbot-Lau X-rayinterferometry (ex. Pfeiffer et al., Nature Physics [1]), and morerecently Far-Field interferometry (Miao et al., Nature Physics [4-5]).

Talbot-Lau X-ray interferometry has made inroads in high contrast phaseand scatter imaging of different materials including animal soft-tissue[1-3]. The interferometry uses coherent X-ray beams passing through aphase-grating and an absorption grating. The X-ray beam after passingthrough the phase-grating generates an interference pattern which isideally directly observed using high resolution (sub-micron) detectors.However to observe the patterns using a standard X-ray detector (ofresolution 15-200 μm) poses a challenge. To overcome this, an absorptiongrating is used as an analyzer. This builds a slow-varying fringepattern. From the intensity of the fringe pattern the object phase-shiftcan be derived. The fringes are a few pixels to a few tens of pixelswide in detectors of resolution 15-200 μm, easily discernable.

Phase-imaging: The change of the voxel-intensity pattern on thestandard-detector with and without the object may then be used tocalculate the phase of the object. With the object in the field theinterference fringes are displaced and from the displacement theobject-phase may be derived. The phase-shifts can be calculated infrequency domain, in a so called single-shot method. With thesingle-shot method, the phase of the object can be resolved at roughlythe width of the fringe pattern (several pixels). To obtain thephase-image within pixel (or even sub-pixel) resolution, aphase-stepping method is used where the analyzer is moved in thetransverse direction in several steps. To summarize, the single shotmethod yields lower resolution, while the phase-stepping yields higherresolution (pixel-level) but requires a higher dose due to multiplesteps.

Dark-field imaging: The Talbot-Lau allows visualizing of scatterers of˜100 nm or less [26]. Scatterers larger than 100 nm will be hard todetect coherently. So called dark field imaging yields the scatterimages. Typically the grating system or the object has to be rotated toobtain the scatter in all directions. A recent work of interest isKagias et al. [24] where a 2D grating with a circular support is used toobtain omni-directional dark-field scatter. This is a single-shottechnique in which the object or the grating system need not be rotatedto obtain the dark field image. Hence, the system has dose advantage.

In [2], a curved detector was used for a hard X-ray (100 keV) Talbot-Lauinterferometer. The circularly aligned structure helps to maximize thefield-of-view [2]. In [25], grating functions bent in a spherical shapewere used for Talbot-Lau interferometry. The radius of the sphericalgrating simulated in [25] was set to 800 mm. The phase grating had aperiodic “on-off” comb structure of 4 μm with a duty cycle of 0.5(transmission line width to period). The design parameters and purposeof the grating was to have increased field-of-view for Talbot-Lauinterferometry.

Far-field interferometry was demonstrated in a recent Nature paper byMiao et al. [5]. Miao et al. [4, 5] showed a far-field system with two(or three) phase-gratings which can display a Moire-pattern ofslow-varying interference fringes (superposed on the high-resolutioninterference pattern). The slow-varying component is directly visible ona standard (low-resolution) X-ray detector without the analyzer. This isa significant development allowing the fringe visualization on astandard detector (15-200 μm resolution), allowing phase contrast X-rayinterferometry at about half the dose of the analyzer-based conventionalTalbot-Lau interferometry [26].

Similar to Talbot-Lau interferometry, the phase can be obtained insingle-shot mode (resolution is low, several pixels) or multi-shotphase-stepping to obtain pixel (or sub-pixel) resolution phase-imaging.

SUMMARY

According to some embodiments of the present disclosure, a phasecontrast X-ray imaging system includes: an illumination source adaptedto illuminate a region of interest; a diffraction grating adapted toreceive illumination from the illuminated region of interest, thediffraction grating comprising a spatial structure having a firstperiodicity superimposed with a second periodicity that is differentfrom the first periodicity; and a detector adapted to detectillumination passing through the diffraction grating, wherein thespatial structure is defined by varying height and/or pitch, and whereinthe spatial structure imparts a first phase dependence based on thefirst periodicity and an additional phase dependence based on the secondperiodicity on the illumination passing through the diffraction grating.

According to some embodiments of the present disclosure, a method forperforming phase contrast X-ray imaging includes: illuminating a regionof interest; receiving illumination from the illuminated region ofinterest; imparting a first phase dependence and a second phasedependence to the received illumination using a single diffractiongrating; and detecting the illumination imparted with the first andsecond phase dependence.

According to some embodiments of the present disclosure, a grating forperforming phase contrast X-ray imaging includes: a support structure;and a plurality of grating elements arranged to receive an X-ray beamtherethrough, wherein the grating is adapted to change the phase of theX-ray beam in a quadratic or spherical-cap form.

BRIEF DESCRIPTION OF THE DRAWINGS

Further objectives and advantages will become apparent from aconsideration of the description, drawings, and examples.

FIG. 1A shows a schematic diagram (not to relative scale) of anembodiment of the invention with some example dimensions for a discretequadratic phase chirp-grating with spatially varying height.

FIG. 1B shows a schematic diagram (not to relative scale) of anembodiment of the invention with some example dimensions for a varyingpitch grating with constant height.

FIG. 1C shows a schematic diagram (not to relative scale) of anembodiment of the invention with some example dimensions for a gratingwith varying height and pitch.

FIG. 2 shows a 2D grating arrangement including a quadratic surface withcircular support. The elements may also be arranged in other patterns,such as hexagonal.

FIG. 3A shows a source, discrete chirp-grating, and flat detector.

FIG. 3B shows a source, discrete chirp-grating, and curved detector.

FIG. 4A shows the entire interference pattern 24.5 cm to 25 cm from thephase grating in steps of 0.5 μm (10,000 lines).

FIG. 4B shows the interference pattern of FIG. 4A zoomed into thesection of interest indicated by the white box in FIG. 4A. Theedge-effects are due to the extent of the grating (4×0.75 mm) 6 mm withrespect to the “detected” intensities (y-direction total of 5 mm).

FIG. 4C shows the interference carpet zoomed further into the section ofinterest.

FIG. 5A shows an example interference line-pattern at 0.5 μm resolutionfrom the carpet (in FIG. 4B). The plot shows intensity along the y-axisof the geometry (FIGS. 3A, 3B). A zoomed section at the center (fewmicrons) is shown for clarity at this resolution.

FIG. 5B shows the (full) line pattern at 15 μm resolution. The fringesare about 23 pixels (0.35 mm) at 15 μm resolution.

FIG. 6A shows an interference line-pattern (zoomed) at 0.5 μm resolutionwith five different delays (0 to 4 μm delay in steps of 1 μm) of thegrating.

FIG. 6B shows the delayed (full) line patterns corresponding to FIG. 6Aat 15 m resolution.

FIG. 7 shows examples of nano/micro-structures built using focused ionbeam (FIB) that had slope and/or a curved surface.

FIG. 8 shows a simulation system diagram.

FIG. 9 shows an interference pattern showing high visibility fringe aty=2.5, z=247.87 detected with 15 μm detector broadening.

FIG. 10 shows the source, linear-quadratic grating, and detector (notrelative to scale). The grating pitch P=500 nm. The peak-to-peak betweenslow-varying component is W=100-200 μm. The maximum heights h1 and h2 ofthe linear and linear-quadratic regions are such that they inducenet-shifts of π/2 and π phase shifts respectively.

FIG. 11 shows an interference pattern at 1-micron resolution for W=0.2mm grating peak-to-peak width. The grating-to-detector distance is 50mm.

FIG. 12 shows an interference pattern at 15-micron resolution for 0.2 mmgrating peak-to-peak width. The grating-to-detector distances is 50 mm.

FIG. 13 shows an interference pattern at 50-micron resolution for 0.2 mmgrating peak-to-peak width. The grating to detector distances is 50 mm.

FIG. 14 shows an interference pattern at 50-micron resolution for 0.1 mmgrating peak-to-peak width. The grating to detector distance is 50 mm.

FIG. 15 shows a system diagram including a detector, a grating, and asource.

FIG. 16A shows a one dimensional rectangular structured grating.

FIG. 16B shows a two directional grating.

FIG. 17A shows, from left to right, a grating, interference pattern in 1μm detector resolution, and interference pattern in 50 μm resolution.The system has 0.1 mm periodicity of rectangular unit grating at 50 mmgrating-to-detector distance.

FIG. 17B shows, from left to right, a grating, interference pattern in 1μm detector resolution, and interference pattern in 50 μm resolution.The system has 0.2 mm periodicity of rectangular unit grating at 50 mmgrating-to-detector distance.

FIG. 18A shows a mammography X-ray source spectrum.

FIG. 18B shows an inference pattern of spectrum in 1 μm resolution at 50mm grating-to-detector distance for a grating with 200 μm rectangularunit period.

FIG. 19A shows a two directional grating with 50 μm periodicity ofrectangular-unit.

FIG. 19B shows a two-dimensional interference pattern at 50 mmgrating-to-detector distance.

DETAILED DESCRIPTION

Some embodiments of the current invention are discussed in detail below.In describing embodiments, specific terminology is employed for the sakeof clarity. However, the invention is not intended to be limited to thespecific terminology so selected. A person skilled in the relevant artwill recognize that other equivalent components can be employed andother methods developed without departing from the broad concepts of thecurrent invention. All references cited anywhere in this specification,including the Background and Detailed Description sections, areincorporated by reference as if each had been individually incorporated.

Phase contrast X-ray provides phase-shift and scatter information inaddition to the attenuation coefficient of material provided byconventional X-ray. This has tremendous consequence for medical imaging,non-destructive testing, and material science. Particularly forsoft-tissue imaging, the real part of the reflective index δ is about˜1000 times the imaginary part β (related to the attenuation), lendingstrong contrast between soft-tissue (that is typically not present inconventional X-ray imaging attenuation coefficient). Of the variousinterferometer techniques, the two at the forefront are far-fieldinterferometry [5] and Talbot-Lau interferometry [1]. While the TalbotLau interferometry has made significant progress, an absorption grating(analyzer) is needed to see interference patterns with standardcost-effective X-ray detectors, a requirement for medical application.The analyzer is detrimental from dose-consideration. Recently far-fieldX-ray [5] eliminated the need for the analyzer by using two (or three)phase-gratings with slight differences in pitch between them to create a“beat-frequency”. The ensuing moire pattern fringes are visible with astandard detector.

An interferometry system is disclosed herein that can achieve the sameresult as Miao et al. (Nature Physics 2015), using a single “chirp”grating (for example, FIG. 1A or a variation of FIG. 10). The gratingfunction has a quadratic phase dependence which will provide alow-frequency intensity component. Other surface approximations such asspherical-cap surfaces may be possible. Sommerfeld-Rayleigh simulationsof the interference carpet were performed. The simulations show thefringes first at 0.5 μm resolution. A slow varying component of thefringe patterns is observed at repeated distance intervals from thegrating. The fringe patterns can be observed at 0.5 μm as well as on alower-resolution 15 μm detector. At 15 μm the fringes are about 23pixels wide (0.35 mm). The system described herein has some of theadvantages of the NIH far-field system [4-5] over Talbot-Lauinterferometry (such as no requirement of an analyzer grating to observefringes with ordinary detectors, thus less dose, etc.) and needs justone grating function. Each prong of the chirp grating can follow thequadratic curve in height or can be approximated as a stepped version(FIG. 1A), i.e., each prong has a constant height, but the heightchanges quadratically from one prong to the next in steps. An on-offpattern, or “combs,” can also be imposed (FIG. 10). The chirp gratingscan lend themselves to 2D extensions with circular supports that can aidin single-shot dark-field imaging.

A grating is described herein which can change the phase of the X-raybeam in a quadratic (or paraboloid) form, proportional to a square of atransverse distance. Other forms such as sections of a sphere, oval, orrectangle may also be used. In paraboloid form the grating is bestdescribed as a “chirp-grating” with the phase varying as square of thedistance. With a deliberate spatial dependence of phase, the followingbenefits are achieved. First, slow-varying components of interferencepatterns superposed on the fast-varying components are obtained to makethe interference fringes visible in a low-resolution X-ray without usingthe absorptive analyzer. Second, since the chirp introduces a quadraticphase, at some distances the X-rays will interfere in phase in a curvedsurface, while others will be in a flat geometry. This allows a curveddetector to be used (optionally), increasing the field of view (FOV) andfringe contrast, which is important for medical applications. Third, the2D version of the grating can have a circular support and be useful for“single-shot” dark-field analysis, similar to the analysis done in [24].The circular support ensures that scatterers in all directions arecaptured. The quadratic phase will ensure that the low-spatially varyingfringes visible in a standard detector are superposed on thefast-varying interference field.

A schematic diagram of an embodiment of the grating is shown in FIG. 1A.The relative dimensions are not to scale (as the height is in micronsand the spatial extent of each element is in mm). The pitch period is500 nm. The key repeating element according to some embodiments hasbase-dimensions of 0.5-2 mm (ex. 0.75 mm) and the grating height (indirection of the beam propagation) varies from 0 to a maximum of π/2 orπ shift. This would imply a few micron to a few 10 s of micron forcommon grating materials such as Au, Si, Cu or Ni. For a 37.8 keV X-raybeam, for example, the height of Si is approximately ˜24.2 μm for a π/2shift and ˜48.4 μm for a π-shift. For Ni the heights are much less, onlyabout ˜6.59 μm and ˜13.19 μm respectively for π/2 and π-shift. Othermaterials are tabulated at a later section. The “height” in FIG. 1A isalong the z-axis, i.e., in the general direction of propagation of lightfrom the source to the detector. As far as the extent in y is concerned,a large extent grating (1 to 20 cm) may be composed as in FIG. 1A byrepeating the key quadratic element. FIG. 1A shows a key grating unitaccording to one embodiment. This is a discrete grating with pitch of500 nm. The grating can also extend along the x-axis, such that thequadratic element has a hemisphere-like shape. FIG. 1B shows a variationin the design of the key element of the grating. For example, thegrating can be designed as a varying pitch grating with constant height(FIG. 1B). In this “1-D” version, the curvature of the grating changesonly in one direction. For the computer simulations the configuration ofFIG. 1A was used with a pitch of 0.5 μm (or 500 nm).

A design difference from work Miao et al. [4, 5] is observed byconsidering the design in FIG. 1A. In Miao et al. [4, 5], the two lineargratings had pitches of a few 100 nm (400 nm and 399 nm) and aslow-varying beat frequency is achieved placing one after the other. Forthe present system in a case for similar pitch, the height of eachelement of the grating is changed in a quadratic manner. This achievesthe slow-varying component for fringe visualization with a standardX-ray detector. Other instances of design differences from Miao et al.[4, 5] are observed by the method of spatially varying the pitch orvarying both the height and the pitch, as shown in the examples in FIGS.1B and 1C.

The grating pattern may be extended to a 2D-grating where 2D“paraboloid” (quadric surface) gratings with circular supports may bedesigned (see FIG. 2).

The phase contrast X-ray imaging system disclosed herein can be usefulfor “single-shot” dark-field analysis, similar to [24]. The circularsupport ensures scatterers in all directions are captured. The quadraticphase will ensure that the low-spatially varying fringes are superposedto the fast-varying interference field to enable visualization withoutthe analyzer.

FIGS. 3A and 3B show a setup for simulation of grating performance. InFIGS. 3A and 3B, the z-axis is the direction of propagation. The gratingplane is in x-y. The Sommerfeld-Rayleigh diffraction integral equationsare used to simulate (see Goodman [27] or Born & Wolfe [28]) the forwardpropagation of the X-ray beam and image formation. Refer to FIGS. 3A and3B for the flat-detector and the curved-detector case, respectively. Thegeneral formation of the image with object is first considered, and thenthe image without object (the reference interference pattern) isconsidered. It is assumed that the chirp grating introduces atransmission and phase delay of the form

G(x,y,z)=T _(G)(x,y,z)exp(jφ _(r)(x,y,z))  (1.1)

where φ_(r)(x,y,z) is in the general form of a quadratic in x and y fora finite support which is then repeated. For the 1-D case, the quadraticdependence is on y for all x.

With the object with a transfer-function T_(O)(x,y,z) exp(jϕ_(O)(x,y,z))inserted together with the grating, the amplitude at the detector isgiven by

$\begin{matrix}{{B( {x_{2},y_{2},z_{2}} )} = {\frac{1}{j\; \lambda}{\int_{G}{{U( P_{S} )}\frac{\exp ( {- {jkr}_{0}} )}{r_{0}}{G( {x_{1},y_{1},z_{1}} )}\frac{\exp ( {- {jkr}_{1}} )}{r_{1}}{T_{O}( {x,y,z} )}{\exp ( {j\; {\varphi_{O}( {x,y,z} )}} )}( {{\hat{r}}_{0} \cdot {\hat{r}}_{1}} ){dx}_{1}{dy}_{1}{dz}_{1}}}}} & (1.2)\end{matrix}$

and the measured intensity is

I(x ₂ ,y ₂ ,z ₂)=|B(x ₂ ,y ₂ ,z ₂)|²  (1.3)

Physically the function means that each point of the detector integratesthe “Huygens” waves emitted at all the grating points.

Simulation of Reference Image

For the reference pattern, the object complex transfer function was setas 1, as it was desired to see the reference pattern without any object.The reference image was simulated with the parameters below. Amonochromatic X-ray source is assumed at 37.8 keV. This corresponds tothe current beamline energy at the Louisiana State University Center forAdvanced Microstructures and Device (CAMD). The transmission isapproximately 1 for the Si dimensions and attenuation through Si atthese energies. The grating is simulated as a phase quadratic functionof y, with phase going from 0 to π/2 μm and then back to zero. Thegrating phase function is sampled in 0.5 μm (y-direction sampling). Thisamounts to a discrete grating in FIG. 1A. Different materials will havedifferent maximum heights. For example, at the maximum height of 24.2μm, Si will provide a π/2 shift of the X-ray beam at 37.8 keV. The totalwidth (extent) of each grating element (along the y direction) was 0.75mm. Four grating elements were simulated for a total of 3 mm gratingwidth (along the y direction). The distance of source to gratingD_(sg)=50 cm (0.5 m). The intensity is then calculated with Eqns. 1.2and 1.3, for all distances 24.5 cm to 25 cm from the grating, in stepsof 0.5 μm. In the y-direction the interference pattern was simulated for5 mm in steps of 0.5 μm. Thus, 100 million intensity values werecalculated in y-z plane, shown in FIG. 4A. The simulation was done on anHPC cluster on multiple nodes.

FIGS. 4A-4C, 5A, and 5B show simulation results. FIG. 4A shows the 100million points of the interference “carpet” for a 5 mm distance between24.5 and 25 cm from the grating. To visualize better, a section of thepattern of interest is taken from the region indicated by a white boxand displayed in FIGS. 4B and 4C with increasing zoom. The slow-varyingfringe patterns are clearly visible in FIG. 4C. The envelope function ofthe interference carpet is shown in FIG. 9 for better visibility.

FIG. 5A shows an extracted line from around ˜247.86 mm of the pattern atFIG. 4C. This is displayed at 0.5 μm. Since at this resolution thousandsof pixels will have to be displayed for the full 5 mm, the line is shownonly for a few microns around the center of y (2.5 mm).

The full (5 mm) pattern is shown next at a 15 μm resolution in FIG. 5B.This is obtained by smoothing with a window and subsampling theinterference pattern at 0.5 μm by factor of 30. FIG. 5B shows the entireline, for 15 μm. A repeating interference pattern at 15 m is clearlyvisible for this design.

FIG. 5B indicates that this system can be used for low-resolution (15μm) fringe detection. At this resolution, each fringe is approximately23 pixels trough-to-trough or about 0.35 mm. For single-shot mechanismtherefore this is the approximate resolution of phase recovery that canbe obtained, which is adequate for phase-image for some applications(such as medical imaging). To obtain the phase to within the resolutionof the pixel-size of the detector or less, the phase-stepping method maybe important.

Phase Stepping Results

The phase of an object can be analyzed in a single shot in the Fourierdomain (to within fringe resolution) or via phase-stepping (pixel orsub-pixel resolution).

The grating according to some embodiments is operated using aphase-stepping method. The grating function can be moved in steps of 1μm, with steps from 0 to 4 μm to evaluate the phase-stepping at the 0.5μm resolution. FIG. 6A shows the delayed patterns at 0.5 μm resolution.The delay is discernable and would be amenable to auto-correlationanalysis. FIG. 6B shows the delay patterns at 15 μm resolution. While atthis resolution the delayed signals are sub-pixel, the signals may beanalyzed with auto-correlation methods. Other delays in steps of 15 μmcan be simulated.

Phase Recovery of an Object

The phase-stepping method can be used to recover the phase of asimulated object. This involves forward simulating with an object andphase-stepping (in steps of 15 μm) with and without the object and usingthe delayed interference lines with and without the object to recoverthe phase using established techniques [6]. The envelope function of theinterference carpet for FIG. 4A is shown in FIG. 9 for bettervisibility.

Grating Design: Grating Materials of Interest

The simulations assumed a 0 to maximum phase shift of π/2. Differentmaterials can be used to achieve the variable phase-shift. The maximumheight for π/2-shift will be reduced successively from Si, Cu, Ni, Au(and hence deposit/etching times). π/2 as well as max-π-shift gratingsare considered. The calculated heights are reported in Table 1. Therefractive index (real-part, δ) was calculated from Eqn. 4 from Mamose[3]. The form-factors as a function of energy and other parametersrequired for the calculation were obtained from the NIST [29].

TABLE 1 Approximate Material Maximum Heights for π/2 and π shifts at37.8 keV Max-Height (μm) π/2 phase- Material shift π phase-shift Gold3.72 7.43 Nickel 6.59 13.19 Copper 6.84 13.68 Silicon 24.20 48.40

Phase contrast X-ray systems provide phase (refractive-index) images andscatter images in addition to transmission images obtained byconventional X-ray. This is independent additional information usefulfor material science, non-destructive imaging and medical imaging todistinguish materials. For example materials with similar attenuationcoefficient will not show significant contrast in conventional X-ray butmay provide discrimination in phase-images or dark-field [4, 25]. Sincesoft-tissue has the phase-shifting refractive index parameter (δ)˜1000times higher than the attenuation component (β), phase-contrast imageswill provide several factors of improved contrast for biomedical imagingand other applications. Scatter imaging for far-field interferometry hasbeen shown to provide excellent images at fraction of dose ofconventional X-ray [4].

All of the advantages of the far-field system [4, 5] over near-fieldTalbot-Lau interferometry holds for the system described herein. Thisincludes (a) elimination of absorption grating (analyzer): directvisualization of fringes in a standard low-resolution X-ray detectorresulting in dose reduction.

Advantages of the system described herein with respect to thestate-of-the-art far-field systems [4, 5] are as follows. A singlegrating is used instead of 2 or 3 typically used [4, 5]. The systemdisclosed herein can be made more compact [30,31] than far-field systems[4,5] which is important for clinical imaging. For example, the systemmay have footprint of a mammogram system, 600 mm, in comparison with thefar-field system [4-5], where the systems are about 1700 mm-2000 mm. Theinterference patterns can be “flat” or “curved” allowing the use ofdifferent shaped detectors. In particular curved detectors may havehigher FOV, useful for medical applications [2]. The design is easilyamenable to 2D grating with paraboloid structures and circular supportwhich will allow for single-shot dark-field imaging, resulting insignificant dose-reduction.

In some embodiments, the far-field systems may require higher lateralsource coherence compared to Talbot-Lau interferometry. However both thestate-of-the-art far-field system [4,5] and Talbot-Lau interferometrysystems [1] has been operative with laboratory X-ray source coupled witha coherence grating. A single phase grating is used in the far-fieldsystem and the design can be more advanced than that in Talbot-Lau.However, since far-field does not need an analyzer, overall cost will beof the same order (or cheaper) even though this system is superiorperformance wise (less dose) than Talbot-Lau interferometry.

The systems and methods described herein may be used for a variety ofphase contrast X-ray applications: non-destructive testing, medicalimaging, and material science, for example. In addition, similar to thefar-field method in [4,5], the system can be adopted for neutronimaging.

Phase contrast X-ray systems can be employed for advanced highresolution non-destructive testing applications such as for space anddefense, and for medical imaging.

Phase contrast X-ray can be used in clinical settings. Thestate-of-the-art far-field system shows significant factor of dosereduction in imaging biological tissue [4] in comparison to currentclinical X-ray, and provides added advantage due to phase and scatterinformation in addition to the conventional transmission image. Thus thesystem has significant potential in the medical domain. According toembodiments, the grating design disclosed herein can be used to helpfacilitate fabrication of large-area gratings for full-body medicalapplications.

Embodiments of the system can be used for non-destructive testing inmaterial science (for example, for applications in defense and space).The interferometry technique and principles described herein can also beimplemented for neutron imaging.

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Sakdinawat, “Ultra-high aspect ratio    high-resolution nanofabrication for hard X-ray diffractive optics,”    Nature Communications, 27 Jun. 2014.-   [24] M. Kagias, Z. Wang, P. Villanueva-Perez, K. Jefimovs, and M.    Stampanoni, “2D-Omnidirectional Hard-X-Ray Scattering Sensitivity in    a Single Shot,” Phys. Rev. Lett. 116, 093902, 3 Mar. 2016.-   [25] W. Cong, Y. Xi and G. Wang, “Spherical grating based X-ray    Talbot Interferometry,” Med Phys, vol. 42, no. 11, pp. 6514-6519,    November 2015.-   [26] Han Wen, “A universal moiré effect and application to X-ray    imaging,” Presentation at LSU, Mar. 3, 2017.-   [27] Introduction to Fourier Optics, J. Goodman, McGraw Hill, 2^(nd)    Ed. 1988.-   [28] Principles of Optics, Electromagnetic Theory of Propagation,    Interference and Diffraction of Light, M. Born and E. Wolf, Pergamon    Press Ltd., 4^(th) Ed, 1970.-   [29] http://physics.nist.gov/PhysRefData/FFast/html/form.html-   [30] J. Dey, J. Xu, K. Ham, N. Bhusal, V. 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EXAMPLES

The following examples describe some embodiments in more detail. Thebroad concepts of the current invention are not intended to be limitedto the particular examples.

Example 1

Phase contrast X-ray represents a break-through in X-ray and CT imaging.In particular, embodiments of the single-phase-grating far-field phasecontrast X-ray system described herein have a strong value propositionfor physicians at hospitals and clinics because they allow moredetailed, higher contrast images to be acquired at a lower X-ray dose.The technology can not only provide all the information of conventionalX-ray (attenuation of tissue), it can also provide two other modalities:phase and scatter. Scatter images provided by the technology are farmore sensitive to structural and density changes of lungs and canidentify lung disease where conventional X-ray fails. Therefore there isan immediate need for diagnostic chest phase contrast X-ray imaging oflung-disease (e.g., COPDs, emphysema, fibrosis, pneumothorax, lungcancer detection and metastasis). Other areas poised to benefit greatlyfrom the system and methods described herein are mammography and bonejoint imaging (e.g., imaging rheumatoid arthritis). Other non-medicalapplications include non-destructive testing (NDT) for battery, oil andgas industry.

Existing phase contrast X-ray products under investigation include asystem developed by NIH investigators Miao et al. [2-3], which uses 2-3phase gratings (instead of one as in the present system) and is costlierand requires higher dose. Additionally, the grating system describedherein can provide single-scan scatter images, which has the clinicaladvantage of reducing the time of the acquisition over the existingproducts.

Immediate Applications

(a) Lung Disease: The systems and methods described herein can fill agap in lung-imaging where conventional X-ray fails to provide adequateinformation. The prevalence of lung diseases in USA alone is in 100 sper 100,000 per year. Example incidence of collapsed lungs(pneumothorax) alone is 26 in 100,000 [23]. Worldwide COPDs killed 3million people in 2015 alone [8]. Greater than 90% of COPDs occur in lowand middle income families [8]. Severe pollution, smoking, etc., being ahigh-risk factor for lung disease, societal need of rapid assessment oflung-disease and treatment is increasing in low income countries and inthe major cities in the developing world like Beijing, Shanghai, NewDelhi, and Kolkata.

(b) Rheumatoid arthritis Imaging: Rheumatoid arthritis is a chronicdisease affecting about 1% of the world population (or ˜74 million),with 1.29 million affected in USA alone [24]. Rheumatoid arthritisimaging involves X-Ray tests to look for signs of bone erosion,inflammation and swelling, tissue damage and overall joint deteriorationin patients. They are used for the detection of rheumatoid arthritissymptoms and in monitoring the progression of the disease over time.

(c) Breast-cancer imaging: In 2014, an estimated ˜3.3 million womenlived with breast cancer in USA alone [25]. The number of new cases offemale breast cancer was 124.9 per 100,000 women per year. Screeningwith mammograms is recommended each year for women over 50.

The most popular phase contrast X-ray system is the near-fieldTalbot-Lau interferometry [4-6, 9-19]. This is the original design fromMomose [5] and Pfeiffer et al. [6]. The systems and methods describedherein are a significant improvement over the nearfield Talbot-Lausystem. The design for a system disclosed herein has several advantagesover Talbot-Lau systems: (a) it does not require an absorption grating,reducing the X-ray radiation dose to the patient (by at least a factorof two); (b) elimination of absorption grating (typically made of gold)also reduces system cost significantly.

The NIH has developed a far-field system [2-3]. However, in comparisonto the NIH system [2-3], the system described herein requires just onegrating instead of 2 or 3. Another aspect is that for dark-field imagingtypically the object or the X-ray system has to be rotated to obtainscatter from all direction. However, the grating described herein canhave a circular support in 2D, providing single-shot (single-scan)dark-field imaging: capturing the X-ray scatter at different angles in asingle scan. This significantly reduces acquisition time of dark-fieldimages.

Thus, the systems and methods described herein can provide a lower-cost,lower-dose, faster system, which is also straight-forward to build(e.g., a single grating instead of several).

According to embodiments, with an adequately large area grating builtfor the application, the grating can be straightforwardly inserted intoa standard X-ray system in between the source and the detector. A direct“no-stepping” integration can allow for resolutions of the order offringe-pitch (0.1-0.4 mm). Better resolution (0.015 mm) may be achievedby inserting a phase-stepping gig such as available in the CAMD system[4] to enable stepping of the grating and processing the changes in theinterference pattern. The system can be incorporated into existing ordeveloping interferometry systems by swapping out optics (phase-grating)and eliminating the absorption grating.

According to embodiments, the phase grating design disclosed hereinrequires a special shape that can be built with existing technology atMicrofabrication centers CAMD and UNC. The required grating fabricationinvolves well established techniques of building optical masks, resistcoating and patterning, electroplating gold and finally using focusedion beam (FIB) to curve out the required shape. FIG. 7 shows examples ofnano/micro-structures built using FIB that had slope and/or a curvedsurface.

Full Sommerfeld-Rayleigh integral simulations were performed of asingle-grating X-ray system with the grating function (schematic in FIG.8). The interference pattern was evaluated at different detectordistances downstream from the grating. Slow varying (near millimeter)patterns were observed at repeated distance intervals from the grating.FIG. 9 shows the interference pattern has exceptionally high visibility,+/−80%, in the center region; the side regions are affected by edgeeffects (due to the small number of gratings used in this initialsimulation). But the ˜30-50% pattern visibility even at the edges(region y<2 mm and y>3 mm) demonstrate the robustness of the gratingdesign. The depth-of-field, roughly 0.1 mm along z, can be tuned withplacement distances and grating parameters but currently matches CTscintillator thickness. The pattern period, 0.35 mm, far exceeds CTdetector resolution (0.015 mm) making this an operational system design.Other necessary design parameters of a successful CT scanner—samplethickness (human thorax), scattering length (lung image contrast)—can bemet by this system design. The system exceeds the performance of thecurrent state of the art system, Miao et al. [2, 3]. The functionalitythat requires 2-3 optics in the design of Miao et al. [2, 3] isaccomplished in one X-ray optic in the systems described herein. Oneoptic means lower cost, lower X-ray dose, and reduced alignmentproblems.

Micro-Fabrication of Grating

Si wafers of required size (for example, 4″ in dimeter) can be depositedwith required metal coating (typically chromium and gold) to make themconductive. Simultaneously, an optical mask can be designed and patternsdefined by different sizes of grating (1.5×1.5 mm; 1.5×3.0 mm; 3.0×3.0mm; 1.5×10 mm) can be fabricated. Dicing lines can also be patternedusing the same mask. Once the patterning is done, gold >3.72 μm can beelectroplated. Then the wafers with metallic coating can be coated witha resist which can be patterned using the optical mask, UV-mask aligner,and other supporting equipment in the cleanroom. The wafer(s) can bediced into pieces (along the dicing lines) of size 30×10 mm, forexample. This can act as a holder of the grating to be mounted on thetomography beamline, for subsequent tests to characterize the fabricatedgrating. The samples can have electroplated gold which can be patternedusing focused ion beam (FIB) to make the required shaped surface. Thiscurved gold structure can act as the phase contrast grating. However,this configuration is provided as an example only, and the embodimentsof the invention are not limited to this configuration for the phasecontrast grating.

REFERENCES FOR EXAMPLE 1

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Pfeiffer, “Grating-based X-ray Dark-field    Computed Tomography of Living Mice,” Ebiomedicine, vol. 2, pp.    1500-1506, 2015.-   [10] Andre Yaroshenko, Tina Pritzke, Markus Koschlig, Nona Kamgari,    Konstantin Willer, Lukas Gromann, Sigrid Auweter, Katharina    Hellbach, Maximilian Reiser, Oliver Eickelberg, Franz Pfeiffer and    Anne Hilgendorff, “Visualization of neonatal lung injury associated    with mechanical ventilation using X-ray dark-field radiography,”    Sci. Rep. 2016; 6: 24269.-   [11] S. B. Hooper, M. J. Kitchen, A. Fouras, N. Yagi, K.    Uesugi, R. A. Lewis, “Long-term Proposal Report 2:Phase Contrast    X-ray Imaging of the Lung,” SPring-8/JASRI, Sayo, Hyogo, Japan, pp.    232-237, vol. 17, 2012.-   [12] S. J. Simpson, K. K. W. Siu, N. Yagi, J. C. Whitley, R. A.    Lewis, P. B. Frappell, “Phase Contrast Imaging Reveals Low Lung    Volumes and Surface Areas in the Developing Marsupial,” PLoS ONE,    vol. 8, no. 1, e53805. doi:10.1371/journal.pone.0053805.-   [13] Huimin Lin, Binquan Kou, Xiangting Li, Yujie Wang, Bei Ding,    Chen Shi, Huanhuan Liu, Rongbiao Tang, Jianqi Sun, Fuhua Yan, Huan    Zhang, “Grating-based Phase-Contrast Imaging of Tumor Angiogenesis    in Lung Metastases,” PLoS ONE, vol. 10, no. 3, e0121438.    doi:10.1371/journal.pone.0121438 pp. 1-12, March 2015.-   [14] J. Tanaka, M. Nagashima, K. Kido, Y. Hoshino, J. Kiyohara, C.    Makifuchi, S. Nishino, S. Nagatsuka, A. Momose, “Cadaveric and in    vivo human joint imaging based on differential phase contrast by    X-ray Talbot-Lau interferometry,” Z. Med. Phys. vol. 23 pp. 222-227,    2013.-   [15] D. Stutman, T. J. Beck, J. A. Carrino, and C. O. Bingham,    “Talbot phase-contrast X-ray imaging for the small joints of the    hand,” Phys Med Biol. vol. 56, no. 17, pp. 5697-5720, 2011.-   [16]A. Tapfer, M. Bech, A. Velroyen, J. Meiser, J. Mohr, M.    Walter, J. Schulz, B. Pauwels, P. Bruyndonckx, X. Liu, A. Sasov,    and F. Pfeiffer. “Experimental results from a preclinical X-ray    phase-contrast CT scanner,” PNAS, 109(39):15691-15696, 2012.-   [17] Kai Scherer, Lorenz Birnbacher, Michael Chabior, Julia Herzen,    Doris Mayr, Susanne Grandl, Anikó Sztrókay-Gaul, Karin Hellerhoff,    Fabian Bamberg, Franz Pfeiffer, “Bi-directional X-ray Phase-Contrast    Mammography,” PLoS ONE, vol. 9, no. 5, e93502, May 2014.-   [18] Z. Wang, N. Hauser, G. Singer, M. Trippel, R. A.    Kubik-Huch, C. W. Schneider, M. Stampanoni, “Non-invasive    classification of micro-calcifications with Phase-Contrast X-ray    Mammography,” Nature Communications vol. 5, no. 3797, May 2014.-   [19] T. Koehler, H. Daerr, G. Martens, N. Kuhn, S. 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Example 2

Phase Contrast X-ray represents a break-through in X-ray and CT imaging.The technology not only provides all the information of conventionalX-ray (attenuation of tissue), it provides two other modalities (phaseand scatter). This has tremendous immediate and long-term significancefor X-ray medical imaging and non-destructive testing.

For soft-tissue imaging, the real part of the reflective index δ isabout ˜1000 times the imaginary part β (related to the attenuation),lending strong contrast between soft-tissue (that is typically notpresent in conventional X-ray imaging attenuation coefficient). Perhapseven more importantly, scatter (dark-field) images provided by thetechnology are far more sensitive to structural and density changes oftissue such as lungs. Phase Contrast X-ray can identify lung diseasewhere conventional X-ray fails [ex. 1-2]. Other areas poised to benefitgreatly are mammography [3-5] and bone joint imaging (e.g., imagingarthritis) [6-7]. Of the various interferometer techniques, the two atthe forefront are Far-field Interferometry [8-9] and Talbot-Lauinterferometry [10-11]. While the Talbot Lau interferometry is the mostwidely adopted and has made clinical progress [ex. 1-7], an absorptiongrating (analyzer) is needed to see interference patterns with standardcost-effective X-ray detectors. The analyzer is detrimental fromdose-consideration. Recently the far-field X-ray interferometry Miao etal. [8-9] eliminated the need for the analyzer by using two (or three)phase-gratings with slight differences in pitch between them to create alow-varying “beat-frequency”. The ensuing moiré pattern fringes aredirectly visible with a standard detector (without analyzer) reducingthe dose [9]. Another important feature of the Miao et al far-fieldinterferometer is that it accesses 2-3 fold better range of scattersthan Talbot-Lau. However one potential drawback is the largesource-to-detector distance necessary: 1730 mm in [9] and about 2000 mmin [8], which will lower X-ray fluence at the detector.

Dey et al. has disclosed a novel design [12] for an X-ray interferometersystem that will achieve interference patterns visible by standarddetectors, using a single phase-grating (along with a source-coherencegrating). The analyzer grating or other phase-gratings are notnecessary. The design can be tuned to a range of differentsource-to-detector distances (ex. 500 mm-1000 mm). Herein, aparallel-beam simulation at 38 keV (CAMD synchrotron beamlinecharacteristics) is disclosed with a detector-to-grating distance of 50mm.

The grating according to some embodiments introduces a deliberatespatial dependence of phase in addition to a linear grating to build upa slow varying fringe pattern on a standard X-ray detector. Theslow-varying spatial function may be quadratic (“chirp”-grating),sinusoid, spherical, etc. A grating design using alternate linear andcurved-linear patterns is shown in FIG. 10.

FIG. 10 shows an illumination source S adapted to illuminate a region ofinterest. A diffraction grating is positioned between the source and thedetector. The grating is adapted to receive illumination from theilluminated region of interest (not shown in FIG. 10). The diffractiongrating has a spatial structure having a first periodicity superimposedwith a second periodicity that is different from the first periodicity.For example, the grating has a period p, as shown in the inset in FIG.10, which may be considered the first periodicity. The grating also hasa variation in height, which is repeated with a second period W that isdifferent from the period p. Alternatively or additionally, the gratingmay have a variation in pitch that is slow as compared to the period p.A detector is adapted to detect illumination passing through thediffraction grating. The spatial structure imparts a first phasedependence based on the first periodicity (p in FIG. 10) and anadditional phase dependence based on the second periodicity (W in FIG.10) on the illumination passing through the diffraction grating.

The base linear grating height (h1) is such that it induces π/2 (in z,the direction of the beam propagation) phase. The curved structure witha varying height induces a 0 to a maximum of π/2. The net maximum is a nshift, corresponding to height h2.

To test this concept full Sommerfield-Rayleigh integral simulations[13-14] of a single-grating X-ray system were performed with analternating linear and linear-quadratic grating function schematicallyshown in FIG. 10. The general formation of the image with the object isconsidered, and then without the object to observe the referenceinterference pattern. The chirp grating is assumed to introduce atransmission and phase delay of the form

G(x,y,z)T _(G)(x,y,z)exp

jφ _(r)(x,y,z)

  (2.1)

where φ_(r)(x,y,z) is in the form of a quadratic in x and y for a finitesupport which is then repeated. For the 1-D case, the quadraticdependence is on y for all x.

The reference pattern at detector is,

$\begin{matrix}{{A( {x_{2},y_{2},z_{2}} )} = {\frac{1}{j\; \lambda}{\int_{G}{{U( P_{S} )}\frac{\exp ( {- {jkr}_{0}} )}{r_{0}}{G( {x_{1},y_{1},z_{1}} )}\frac{\exp ( {- {jkr}_{1}} )}{r_{1}}( {{\hat{r}}_{0} \cdot {\hat{r}}_{1}} ){dx}_{1}{dy}_{1}{dz}_{1}}}}} & (2.2)\end{matrix}$

and the measured intensity is

I(x ₂ ,y ₂ ,z ₂)=|A(x ₂ ,y ₂ ,z ₂)|²  (2.3)

Physically the function means each point of the detector “sees”(weighted with obliquity factor) and superposes the “Huygens” waveemitted from all the grating points.

“Reference” Pattern: The reference image was simulated with theparameters below. A monochromatic X-ray source is assumed at 37.8 keV.The source beam is assumed parallel. This corresponds to the currentbeamline at CAMD. But even for an X-ray tube-source (with coherencegrating), paraxial approximation may be used and a parallel beamconfiguration of each spherical wave may be adopted [13, 16]. For thephase-grating to detector the spherical wave exp(−jkr₁)/r₁ is usedwithout approximation in simulation.

The linear-quadratic grating phase function is sampled with 1 nmsampling (y-direction sampling). FIG. 11 (bottom) shows the extent ofthe grating function (1.2 mm) with the width W=200 am. The intensity isthen calculated with Eqns. 2.2 and 2.3, for grating-to-detector distanceD_(dg)=50 mm. The slow varying patterns at 1 μm are shown in FIG. 11(top). The peak-to-peak distance is 200 μm. The interference carpet wassmoothed and subsampled at the 15 μm (0.015 mm) CAMD interferometry CTresolution and shown in FIG. 12. The pattern period, 0.2 mm, exceeds theCAMD interferometer CT detector resolution (15 μm) or the 50 μm detectorresolution used in mammogram system [5] making this an operationalsystem design. FIG. 13 shows the pattern with 50 μm resolution.

The simulator can be generalized by modeling spatially extendedpolychromatic source for modeling laboratory X-ray tube. A complexobject transfer function (with transmission and phase) may be insertedbetween source and grating or grating and detector in Eqn. 2.2.

FIG. 14 demonstrates that the interference pitch visible in the detectormay be controlled by changing the grating pattern. If the W is halvedthe interference pitch is halved as well. Note that the fringe contrastis excellent but one caveat is that for some systems, scatter andde-coherence due to polychromacity of X-ray tube source may affect thefringe contrast.

A novel single-phase-grating far-field phase contrast system wassimulated using Sommerfield-Rayleigh diffraction integrals. In one X-rayoptic functionality it is accomplished that requires 2-3 optics in theMiao et al. design [8-9]. The benefits of not requiring the absorptiongrating (analyzer) in Talbot-Lau interferometers is retained. This willreduce the dose-requirement (by a factor of two). Also, reducing themultiple gratings of Miao et al. to a single grating significantlyreduces the space required to enclose the system, as well as thestrength of the X-ray tube required to acquire an image. Using thesystem described herein, an interference pattern (pitch 0.2 mm) wasobserved for a grating-to-detector distance of 50 mm for a parallelX-ray source. The interference pattern can be tuned to differentapplications depending on detector resolution.

REFERENCES FOR EXAMPLE 2

-   [1] A. Velroyen, A. Yaroshenko, D. Hahn, A. Fehringer, A. Tapfer, M.    Müller, P. B. Noël, B. Pauwels, A. Sasov, A. Ö. Yildirim, O.    Eickelberg, K. Hellbach, S. D. Auweter, F. G. Meinel, M. F.    Reiser, M. Bech, F. Pfeiffer, “Grating-based X-ray Dark-field    Computed Tomography of Living Mice,” Ebiomedicine, vol 2, pp.    1500-1506, 2015.-   [2] Andre Yaroshenko, Tina Pritzke, Markus Koschlig, Nona Kamgari,    Konstantin Willer, Lukas Gromann, Sigrid Auweter, Katharina    Hellbach, Maximilian Reiser, Oliver Eickelberg, Franz Pfeiffer and    Anne Hilgendorff, “Visualization of neonatal lung injury associated    with mechanical ventilation using X-ray dark-field radiography,” Sci    Rep. 2016; 6: 24269.-   [3] Kai Scherer, Lorenz Birnbacher, Michael Chabior, Julia Herzen,    Doris Mayr, Susanne Grandl, Anikó Sztrókay-Gaul, Karin Hellerhoff,    Fabian Bamberg, Franz Pfeiffer, “Bi-directional X-ray Phase-Contrast    Mammography,” PLoS ONE, vol. 9, no. 5, e93502, May 2014.-   [4] Z. Wang, N. Hauser, G. Singer, M. Trippel, R. A.    Kubik-Huch, C. W. Schneider, M. Stampanoni, “Non-invasive    classification of micro-calcifications with Phase-Contrast X-ray    Mammography,” Nature Communications vol. 5, no. 3797, May 2014.-   [5] T. Koehler, H. Daerr, G. Martens, N. Kuhn, S. Löscher, U van    Stevendaal, E, Roessl, “Slit-scanning differential X-ray    phase-contrast mammography: Proof-of-concept experimental studies,”    Med. Phys. vol. 42, no. 4, pp. 1959-1965, April 2015.-   [6] J. Tanaka, M. Nagashima, K. Kido, Y. Hoshino, J. Kiyohara, C.    Makifuchi, S. Nishino, S. Nagatsuka, A. Momose, “Cadaveric and in    vivo human joint imaging based on differential phase contrast by    X-ray Talbot-Lau interferometry,” Z. Med. Phys. vol. 23, pp.    222-227, 2013.-   [7] D. Stutman, T. J. Beck, J. A. Carrino, and C. O. Bingham,    “Talbot phase-contrast X-ray imaging for the small joints of the    hand,” Phys Med Biol. vol. 56, no. 17, pp. 5697-5720, 2011.-   [8] H. Miao, A. A. Gomella, K. J. Harmon, E. E. Bennett, N.    Chedid, S. Znati, A. Panna, B. A. Foster, P. Bhandarkar and H. Wen,    “Enhancing Tabletop X-Ray Phase Contrast Imaging with    Nano-Fabrication,” Scientific Reports, vol. 5, No. 13581, August    2015 DOI: 10. 1038/srep13581.-   [9] H. Miao, A. Panna, A. A. Gomella, E. E. Bennett, S. Znati, L.    Chen and H. Wen, “A universal moiré effect and application in X-ray    phase-contrast imaging,” Nature Physics, vol. 12, pp. 830-834, April    2016.-   [10] A. Momose, “Recent Advances in X-ray Phase Imaging,” Japanese    Journal of Applied Physics, Vol. 44, No. 9A, 6355-6367, 2005.-   [11] F. Pfeiffer, T. Weitkamp, O. Bunk and C. David, “Phase    retrieval and differential phase-contrast imaging with    low-brilliance X-ray sources,” Nature Physics vol. 2, April 2006,    (www.nature.com/naturephysics, published online: 26 Mar. 2006).-   [12] J. Dey et al., LSU Disclosure LSU-2017-034, March 2017.-   [13] Introduction to Fourier Optics, J. Goodman, McGraw Hill, 2^(nd)    Ed. 1988.-   [14] Principles of Optics, M. Born and E. Wolf, Pergamon Press Ltd,    1970.-   [15] S. Marathe, L. Assoufid, X. Xiao, K. Ham, W. W. Johnson,    and L. G. Butler, “Improved Algorithm for Processing Grating-Based    Phase Contrast Interferometry Image Sets,” Rev. Sci. Instrum., vol.    85, no. 013704, 2014.-   [16] H. Wen, C. K. Kemble, E. E. Bennett, “Theory of Oblique and    Grazing Incidence Talbot-Lau Interferometers and Demonstration in a    Compact Source X-ray Reflective Interferometer,” Optics Express,    vol. 19, no. 25, pp. 25093-25112, 2011.

Example 3

Phase contrast X-ray not only provides conventional tissue attenuationprovided by regular X-ray and CT, it can provide images based on X-rayphase-shift and scatter (dark-field), within the same scan. PhaseContrast X-ray can identify lung disease where conventional X-ray fails[ex. 1-2]. Other areas poised to benefit greatly are mammography [3-5]and bone joint imaging (e.g., imaging arthritis) [6-7]. The twointerferometry methods currently at the forefront are: Far-fieldInterferometry (Miao et al., Nat. Phy. 2015; Sci Rep 2015) [8-9]) andTalbot-Lau interferometry (Momose JJAP 2005, Pfeiffer Nature 2006[10-11]). While Talbot Lau interferometry has made the most clinicalstride [ex. 1-7], an absorption grating (analyzer) is needed to seeinterference patterns with standard cost-effective X-ray detectors,which is detrimental from dose consideration. Recently the far-fieldX-ray interferometry Miao et al. [8-9] eliminated the need for theanalyzer by using two (or three) phase-gratings with slight differencesin pitch between them to create a low-varying “beat-frequency.” Theensuing moiré pattern fringes are directly visible (without analyzergrating) with a standard detector reducing dose 2-folds [9]. A mostimportant feature of the far-field interferometer is that it accesses 2to 3-folds better range of scatter than Talbot-Lau. The ˜400 nm pitch ofthe phase grating makes Miao et al. [8-9] system a far-field systemrather than near-field system like the Talbot-Lau [10-11]. One drawbackis that the 2-3 phase-gratings in [8-9] have to be aligned and placed atfine-tuned distances to obtain fringe patterns. Also thesource-to-detector distances are 1.7-2 m for the Miao et al systems[8-9].

Described herein is a clinically practical near-field system that uses asingle phase grating. This achieves similar results as Miao et al [8]and is also compact. Initial linear-quadratic gratings were presented in[12]. Herein, a slow rectangular pattern superposed on a linear-gratingis presented. This simpler grating is easier to manufacture. Moreover,mono-directional grating phase contrast imaging cannot be isotropic insensitivity at every direction to diagnose high oriented tissuestructures, like fine tumor branches of invasive ductal carcinoma.Typically, bi-directional (90° rotation of mono-directional grating)acquisitions are applied accordingly to obtain phase information in twoorthogonal directions [3]. To acquire phase contrast imaging withisotropic sensitivity in a single shot, a two-dimensional structuredgrating is also described herein. In this work, both one-dimensional andbi-directional gratings are simulated using Sommerfeld-Rayleighequations [13-14] to show feasible systems with strong discernablefringes 50 mm away from gratings.

A grating is disclosed herein with a slow-varying function (rectangularin this instance) of repeating phase-dependence superposed on thegrating pattern. Such a function maybe achieved by gradually changingthe spatial height of the grating. This will create sampling patterns orfringes with the spacing required to image with standard CT/X-raydetector resolution. A system shown in FIGS. 15, 16A, and 16B issimulated. The rectangular grating structures are shown in FIGS. 16A and16B. FIG. 16A shows the one-dimensional case and FIG. 16B shows thetwo-directional case. Each rectangle has a grating pattern 800 nm pitchand 50% duty-cycle. The 800 nm pitch of the grating pattern makes this anear-field system. The period of interference fringes (peak-to-peakwidth) can be adjusted by varying periodicity (peak-to-peak width W) ofrectangular units in grating. The reference amplitude at detector isobtained by evaluating the Sommerfeld-Rayleigh [13-14] integral givenby,

$\begin{matrix}{\mspace{79mu} {{G( {x,y,z} )} = {{T_{G}( {x,y,z} )} \cdot e^{{- i}\; {\phi_{r}{({x,y,z})}}}}}} & (3.1) \\{{A( {x_{2},y_{2},z_{2}} )} = {\frac{1}{i\; \lambda}{\int{\int{\int{{{U( P_{S} )} \cdot \frac{e^{- {ikr}_{0}}}{r_{0}} \cdot {G( {x_{1},y_{1},z_{1}} )} \cdot \frac{e^{- {ikr}_{1}}}{r_{1}} \cdot ( {r_{0} \cdot r_{1}} )}{dx}_{1}{dy}_{1}{dz}_{z}}}}}}} & (3.2)\end{matrix}$and the intensity is I(x ₂ ,y ₂ ,z ₂)=|A(x ₂ ,y ₂ ,z ₂)|²  (3.3)

where U(P_(s)) is the source, assumed as a parallel beam of X-ray. Thegrating-to-detector distance was 50 mm. The design energy used was 17.5keV. To evaluate the intensity, the grating function G(x₁, y₁, z₁) issampled at 1 nm and the detector is sampled at 1 μm. Interferencepatterns are simulated for a range of height pairs (h₁, h₂)corresponding to phase-shifts (π/4, π/2) to (π/2, π).

To image an object with this system, the interference pattern has to beimaged single shot with and without object or multiple exposures forphase-stepping methods [15]. Direct Fourier method [16] can use used forthe single-shot acquisition (with and without object) to obtain thephase of the object. The shape, spacing, and maximum-height can bevaried to provide compact designs with control over the fringe contrastover different detector distances. For instance, the rectangular unitcan also be replaced by quadratic (paraboloid) shape superposed on alinear structure. Certainly, the linear-rectangular grating is easier inmanufacture.

The results of the detector simulation for one dimensionallinear-rectangular structured grating case are shown in FIGS. 17A and17B. FIG. 17A shows an interference pattern of 100 μm rectangular unitperiod in grating with 1 μm and 50 μm resolution at 50 mmgrating-to-detector distance. The peak-to-peak width of interferencefringes is 100 μm. FIG. 17B shows an interference pattern of 200 μmrectangular unit period in grating with 1 μm and 50 m resolution at 50mm grating-to-detector distance. The peak-to-peak width of interferencefringes is 200 μm.

Moreover, X-ray sources in clinical applications generate continuousenergy spectrums rather than monoenergetic output. To clarify the effectof partially losing longitudinal coherence to interference patterns, asimulation is accomplished of a linear-rectangular grating in 200 μmunit period with an X-ray spectrum used in mammography. For simplicity aparallel beam approximation is used. FIG. 18A shows the X-ray spectrumgenerated with 30 kV peak tube voltage, molybdenum anode and 0.2 mmthickness molybdenum filter (by Siemens Healthcare Simulation of X-raySpectra online tool). The corresponding simulation results ofinterference pattern is showed in FIG. 18B with 1 μm resolution at 50 mmgrating-to-detector distance.

The simulation results of two-directional rectangular-linear grating areshowed in FIGS. 19A and 19B. FIG. 19A shows the plan view of the gratingwith both 50 m periodicity of rectangular unit in X and Y directions.FIG. 19B shows the two-dimensional interference pattern with 50 mmgrating-to-detector distance. The fringes still keep 50 μm peak-to-peakwidth, which means for the rectangular-linear structured phase gratingin two directional case, the interference pattern is also controlled andadjustable like one-dimensional cases.

The design disclosed herein exceeds the performance of the one of thebest systems, Miao et al. far-field system [8,9]. In one X-ray opticfunctionality is accomplished that requires 2-3 optics in their design.The system disclosed herein has more control over the fringe contrast atcompact detector distances and can be fine-tuned to differentapplications by changing the shape, spacing and maximum-height of thegratings. All the benefits of Miao et al. far-field system of notrequiring analyzer over Talbot-Lau interferometers are retained.

A feasible and compact phase contrast X-ray system is shown with atwo-dimensional single phase-grating, requiring no analyzer. The designuses a single grating instead of a 2-3 phase gratings in one of thecurrent best systems, Miao et al. The system disclosed herein retainsall the advantages of a far-field system—(a) requiring no analyzerunlike the Talbot-Lau system [10,11]; this will reduce dose by a factorof ˜2 and (b) the system disclosed herein provides compact designs withmore control over the fringe contrast at different detector distances.

REFERENCES FOR EXAMPLE 3

-   [1] A. Velroyen A. Yaroshenko, D. Hahn, A. Fehringer, A. Tapfer, M.    Miller, P. B. Noël, B. Pauwels, A Sasov, A. Ö. Yildirim, O.    Eickelberg, K. Hellbach, S. D. Auweter, F. G. Meinel, M. F.    Reiser, M. Bech, F. Pfeiffer, Ebiomedicine, vol 2, 2015.-   [2] A. Yaroshenko, T. Pritzke, M. Koschlig, N. Kamgari, K.    Willer, L. Gromann, S. Auweter, K. Hellbach, M. Reiser, O.    Eickelberg, F. Pfeiffer et al., Sci Rep, vol. 6 2016.-   [3] K. Scherer, L. Birnbacher, M. Chabior, J. Herzen, D. Mayr, S.    Grandl, A. Sztrókay-Gaul, K. Hellerhoff, F. Bamberg, F. Pfeiffer,    PLoS ONE, vol. 9, no. 5, e93502, May 2014.-   [4] Z. Wang, N. Hauser, G. Singer, M. Trippel, R. A.    Kubik-Huch, C. W. Schneider, M. Stampanoni, Nature Communications,    vol. 5, no. 3797, May 2014.-   [5] T. Koehler, H. Daerr, G. Martens, N. Kuhn, S. Löscher, U.    Stevendaal, E. Roessl, Med. Phys. vol. 42 no. 4, pp. 1959-1965,    April 2015.-   [6] J. Tanaka, M. Nagashima, K. Kido, Y. Hoshino, J. Kiyohara, C.    Makifuchi, S. Nishino, S. Nagatsuka, A. Momose, Z. Med. Phys. vol.    23, pp. 222-227, 2013.-   [7] D. Stutman, T. J. Beck, J. A. Carrino, and C. O. Bingham, Phys    Med Biol. vol. 56, no. 17, pp. 5697-5720, 2011.-   [8] H. Miao, A. Panna, A. A. Gomella, E. E. Bennett, S. Znati, L.    Chen and H. Wen, Nature Physics, vol. 12, pp. 830-834, April 2016.-   [9] H. Miao, A. A. Gomella, K. J. Harmon, E. E. Bennett, N.    Chedid, S. Znati, A. Panna, B. A. Foster, P. Bhandarkar and H. Wen,    Scientific Reports, vol. 5, No. 13581, August 2015.-   [10] A. Momose, Japanese Journal of Applied Physics, vol. 44, no.    9A, pp. 6355-6367, 2005.-   [11] F. Pfeiffer, T. Weitkamp, O. Bunk and C. David, Nature Physics,    vol. 2, April 2006, (www.nature.com/naturephysics, published online:    26 Mar. 2006).-   [12] J. Dey, J. Xu, K. Ham, N. Bhusal, V. Singh, “A Novel Phase    Contrast System,” presentation, IEEE NSS-MIC, October 2017 (oral).-   [13] J. Goodman, “Introduction to Fourier Optics,” McGraw Hill,    2^(nd) Ed. 1988.-   [14] M. Born and E. Wolf, “Principles of Optics,” Pergamon Press    Ltd, 1970.-   [15] S. Marathe, L. Assoufid, X. Xiao, K. Ham, W. W. Johnson,    and L. G. Butler, Rev Sci Instrum, vol. 85, no. 013704, 2014.-   [16] N. Bevins, J. Zambelli, K. Li, Z. Qi, G-H Chen, Med Physics,    vol. 39, no. 1, pp. 424-428, 2012.

The embodiments illustrated and discussed in this specification areintended only to teach those skilled in the art how to make and use theinvention. In describing embodiments of the invention, specificterminology is employed for the sake of clarity. However, the inventionis not intended to be limited to the specific terminology so selected.The above-described embodiments of the invention may be modified orvaried, without departing from the invention, as appreciated by thoseskilled in the art in light of the above teachings. It is therefore tobe understood that, within the scope of the claims and theirequivalents, the invention may be practiced otherwise than asspecifically described.

We claim:
 1. A phase contrast X-ray imaging system comprising: anillumination source adapted to illuminate a region of interest; adiffraction grating adapted to receive illumination from the illuminatedregion of interest, the diffraction grating comprising a spatialstructure having a first periodicity superimposed with a secondperiodicity that is different from the first periodicity; and a detectoradapted to detect illumination passing through the diffraction grating,wherein the spatial structure is defined by varying height and/or pitch,and wherein the spatial structure imparts a first phase dependence basedon the first periodicity and an additional phase dependence based on thesecond periodicity on the illumination passing through the diffractiongrating.
 2. The phase contrast X-ray imaging system according to claim1, wherein the diffraction grating imparts a position-dependentquadratic phase, wherein the position-dependent quadratic phase isproportional to a square of a transverse distance from a pre-determinedposition on the diffraction grating in a first dimension.
 3. The phasecontrast X-ray imaging system according to claim 1, wherein thediffraction grating imparts a position-dependent quadratic phase,wherein the position-dependent quadratic phase is proportional to asquare of a transverse distance from a pre-determined position on thediffraction grating in a first dimension and in a second dimension. 4.The phase contrast X-ray imaging system according to claim 1, whereinthe grating imparts a position-dependent spherical phase.
 5. The phasecontrast X-ray imaging system according to claim 1, wherein thediffraction grating includes a plurality of grating elements, whereinthe grating elements have a varying pitch that imparts the additionalphase dependence on the illumination passing through the diffractiongrating.
 6. The phase contrast X-ray imaging system according to claim1, wherein the diffraction grating contains a plurality of gratingelements, wherein the grating elements have a varying pitch and avarying height, wherein the varying pitch and the varying height impartthe additional phase dependence on the illumination passing through thediffraction grating.
 7. The phase contrast X-ray imaging systemaccording to claim 1, wherein the system does not include an absorptiongrating.
 8. The phase contrast X-ray imaging system according to claim1, wherein the illumination passes through a single grating before beingdetected by the detector.
 9. The phase contrast X-ray imaging systemaccording to claim 1, wherein the detector is curved.
 10. The phasecontrast X-ray imaging system according to claim 1, wherein thediffraction grating has a circular support, and wherein the phasecontrast X-ray imaging system is used to perform single-shot dark-fieldimaging.
 11. The phase contrast X-ray imaging system according to claim1, further comprising a display device configured to display an image ofthe region of interest using the detected illumination.
 12. A method forperforming phase contrast X-ray imaging, comprising: illuminating aregion of interest; imparting a first phase dependence and a secondphase dependence to the received illumination using a single diffractiongrating; and detecting the illumination imparted with the first andsecond phase dependence.
 13. The method for performing phase contrastX-ray imaging according to claim 12, further comprising: displaying animage of the region of interest using the detected illumination.
 14. Agrating for performing phase contrast X-ray imaging, comprising: asupport structure; and a plurality of grating elements arranged toreceive an X-ray beam therethrough, wherein the grating is adapted tochange the phase of the X-ray beam in a quadratic or spherical-cap form.15. The grating for performing phase contrast X-ray imaging according toclaim 14, wherein the plurality of grating elements has a varying pitchthat imparts a phase dependence on illumination passing through thegrating.
 16. The grating for performing phase contrast X-ray imagingaccording to claim 14, wherein the plurality of grating elements has avarying pitch and a varying height, wherein the varying pitch and thevarying height impart a phase dependence on illumination passing throughthe grating.
 17. The grating of claim 14, wherein the height of eachgrating element has a quadratic dependence on a position of the gratingelement with respect to an edge of the grating, wherein the quadraticdependence achieves a slow-varying component for fringe visualizationwith a standard X-ray detector, the slow-varying component havingfringes that are a few pixels to a few tens of pixels wide in thestandard X-ray detector.
 18. The grating of claim 14, wherein thesupport is a circular support, and wherein the grating elements form aparaboloid shape.
 19. The grating of claim 14, wherein each of theplurality of grating elements has a transverse width of about 0.5 mm toabout 2 mm, and wherein a height of the plurality of grating elementsvaries from a height corresponding to a 0 phase shift to a heightcorresponding to a π/2 phase shift of the X-ray beam.
 20. The grating ofclaim 14, wherein each of the plurality of grating elements has atransverse width of about 0.5 mm to about 2 mm, and wherein the heightof the plurality of gratings varies from a height corresponding to a 0phase shift to a height corresponding to a it phase shift of the X-raybeam.